Algebra One As of: September 2014 Teacher Contact: Ms.Zinn (CVHS-NGC) CCSS Unit Theme SKILLS ASSESSMENT & PRODUCTS Translate sentences into equations such as, The length of a rectangle is ten less than the width. Translate equations into written sentences. Write equations or expressions to model and solve problems. Write let statements to define variables when modeling real-world problems. September equations Solve multi-step equations. Tell which property or identity is being used in each step to simplify an expression or solve an equation. Identify the additive inverse (opposite) or multiplicative inverse (reciprocal) of a number. Verify if the commutative property works for any operation. For example, does a-b = b-a? Verify if the associative property works for any operation. For example, does (xy)z = (xz)y? Write variable expressions to represent even or odd integers. Solve consecutive integer problems algebraically. Solve equations involving CLT, distribution or variables on both sides. Solve for missing values in proportions, especially when the missing value is part of a binomial. Write proportions to model applied situations. Solve an equation for a specific variable. For example, solve E = mc 2 for c. Use formulas to solve problems. Classify numbers as whole numbers, integers, rational numbers, irrational numbers, real numbers or imaginary.
October/No vember linear functions Identify key features of a linear function (shape, y-intercept, x-intercept, slope or rate of change, domain and range). Transition between different representations of functions: real-world scenario, table, graph and equation. Given a table, graph or scenario, identify the domain, range, independent variable, dependent variable and rate of change. Graph a linear equation in slope-intercept form without using a table. Given a linear equation, identify its slope and y-intercept. Given two points, calculate the slope of a line through those points. Given one point and the slope, graph the line and write its equation or given two points, write the equation of a line in slope-intercept form. Identify if an equation or graph models a proportional relationship. Identify the unit rate of a proportional relationship. Graph horizontal and vertical lines. Write equations for horizontal or vertical lines Make a scatter plot. Identify positive, negative or no correlation. Classify correlations as strong or weak. Use technology to find correlation coefficient. Discuss the use of correlation coefficient as a way to measure strength of linear association. Differentiate between correlation and causation. Find the line of best fit for a scatter plot by hand. Use representations of linear relationships to analyze information, make predictions and solve problems. Graph an equation in point-slope form. Write the equation of a line in point-slope form. Graph an equation in standard form. Write the equation of a line in standard form. Convert equations in point-slope form or standard from into slope-intercept form. Model real-world situations with equations in standard form or point-slope form. Identify parallel or perpendicular lines from their equations. Identify parallel or perpendicular lines from their graphs (using slope). Use the symbols for parallel and perpendicular. Write an equation for a line through a point and parallel to another line. Write an equation for a line through a point and perpendicular to another line. Identify the equations that make the line segments for right angles and parallel lines in quadrilaterals and right triangles. (optional enrichment)
systems of linear equations review semester exam Given a system of equations, determine the number of solutions. Solve systems of equations by graphing. Solve systems of equations by substitution. Solve systems of equations by the addition/subtraction method. (elimination with or without multiplication) Write systems of equations to solve problems. Evaluate which method is the best method to solve a given system of equations. Understand how and when to use empty set and all real numbers as the solution to a system of equations.
Know the parent function, name and shape of the following families of functions. f (x)= mx+b [including f (x) = c] f (x) = x 2 f (x) = x f (x) = x 3 f (x) = 3 x f (x) = x f (x) = a x f (x) = x 1 Recognize and continue patterns. Determine if a relation is a function. Identify the domain and range of a function. Identify if a function is increasing or decreasing over its entire domain. Tell if a function has an inverse. If it does, write the inverse of a function. Recognize simple inverse pairs, such as f (x) = x 3 and f (x) = 3 x or (1, 5) and (5 1). (Section 4-3 in 2005 text, section 3-1 in 2008 text). Identify the x and y-intercepts of a function. Identify the critical points (relative max and min) for a function. December families of functions Identify the horizontal asymptotes of exponential functions. Identify the horizontal and vertical asymptotes of rational functions (the x and y axes for the parent function). Understand the difference between directly and inversely proportional relationships. Apply transformations to parent functions and represent symbolically. Classify functions as having reflectional or rotational symmetry (or neither) Classify functions as linear, quadratic, cubic or exponential based on first, second or third differences or common ratios. Transition between real-world scenario, table, graph or equation to model a situation. Identify the family of a function best suited for modeling a given real-world situation. Model real-world situations with a function. Use representations of different functions to analyze information, make predictions and solve problems.
Solve multistep inequalities. Define variables and write inequalities to model real-world scenarios. Graph one-variable inequalities on a number line ( for example -1 < a where variables is not on the left side of the symbol). Evaluate expressions involving absolute value. (Evaluate expressions using the order of operations (P, E, M or D, A S) given values for variables). Interpret representations that reflect absolute value relationships. Solve absolute value equations and inequalities. January February inequalities and absolute value Graph inequalities involving absolute value on a number line or coordinate plane. Rewrite 2-variable inequalities in slope intercept form. Graph one or two-variable inequalities on the coordinate plane. Determine if an ordered pair is part of the solution set of a two-variable inequality. Graph systems of inequalities in 2-variables. cumulative exam semester one Determine if an ordered pair is part of the feasible region for a system of inequalities. Graph piecewise functions Given the graph of a piecewise function, write the set of equations that define it. Graph absolute value functions. Identify key features of an absolute value function such as vertex, domain and range, line of symmetry and maximum or minimum. Identify the portions of an absolute value function that are increasing or decreasing. Translate absolute value functions from the parent function.
Apply exponents to positive numbers. Evaluate to exact value. Use negative exponents, fractional exponents, exponents greater than one; use an exponent of zero. Transition easily between roots and exponents. Specifically, calculate square roots or cube roots of perfect squares and cubes and up to 5 th roots for powers of 2 and 3 without a calculator. Use rules of exponents, singularly or in combination. a x product rule x a x b = x a+b, quotient rule = x a-b, power-to-power rule (x a ) b = x ab b x Classify numbers as whole numbers, integers, rational, irrational, real or imaginary. February exponential functions Differentiate between exact value and approximation. For example, 1/9 is the exact value and 0.1 is the approximate value. Identify perfect squares and perfect cubes. Evaluate expressions using the order of operations (P, E, M or D, A S) given values for variables. Write exponential equations given the initial value and rate of growth. Sketch the graph of exponential equations given the initial value and rate of growth. Identify the defining characteristics of the graph of an exponential function: y-intercept, shape and horizontal asymptote. Identify the end behavior of the graph of an exponential function. Differentiate between exponential growth or decay based on the equation or the graph. Calculate percent change and use this information to solve problems. Transition between real-world scenario, table, graph or equation to model a situation. Use representations of exponential relationships to analyze information, make predictions and solve problems.
Write polynomials in ascending or descending order. Classify expressions as monomials, binomials, trinomials and/or polynomials. Combine like monomials. Multiply a monomial by a polynomial (distribution). Multiply two binomials. March factoring Write expressions or equations to represent the perimeter, area or volume of simple two or three dimensional shapes. Use equations for the perimeter, area or volume to solve for measures of missing variables or sides. Find all the factor pairs for an integer. Find the greatest common factor between two monomials. Factor polynomials by reverse distribution of the GCF. Factor trinomials of the form 0 = x 2 + bx + c. Factor trinomials of the form 0 = ax 2 + bx + c, where a is not a factor of all terms. Factor 4 term polynomials by grouping. Factor the difference of two squares.
April Quadratics Part 1: standard form factored form Part 2: vertex form complete the square Identify quadratic equations and the shape of their graphs. Use a table of values to graph quadratic equations. Evaluate expressions using the order of operations (P, E, M or D, A S) given values for variables. Recognize and continue patterns. Determine if a parabola opens up or down from its equation. Determine if a parabola has a maximum or minimum. Identify the axis of symmetry for a parabola as an equation. (For example, x = 4). Tell which portions of the function are increasing or decreasing. Identify the vertex as an ordered pair. Understand the effects of degree, leading coefficient and number of real zeros on the graphs of polynomial functions of degree greater than two. Identify the maximum number of zeros (x-intercepts) of a function. Understand the relationship between x-intercepts of a graph and the factored form of the function. Associate a given equation with the function whose zero(s) is/are the solution(s) to the equation. Solve or find the x-intercepts of a quadratic equation by quadratic formula. Solve a system of one (oblique) linear and one quadratic function. Graph quadratic equations based on their quantitative characteristics from vertex form, standard from or factored form. Associate a given equation with the function whose zero(s) is/are the solution(s) to the equation. Transition between real-world scenario, table, graph or equation to model a situation. Use representations of quadratic relationships to analyze information, make predictions and solve problems. Identify the domain and range of a quadratic function. Given a quadratic function in vertex form, identify the line of symmetry, vertex, y-intercept, domain, range, and portions that are increasing or decreasing. Graph quadratic equations that are given in vertex form. Given a graph of a parabola, write the equation in vertex form. Solve vertex form equations to determine x-intercepts. Identify a perfect square trinomial. Given an expression in standard form, ax 2 +bx+c, find values of b or c to create a perfect square trinomial. Use CTS to change an equation from standard form to vertex form. Determine the a value in y = a (x h) 2 + k by substituting a point on the graph and the vertex into the vertex form equation. Tell if a function has been moved from the parent function: direction (right, left, up or down) and magnitude (how far). Given a description of a graph, be able to write the equation in vertex form.
May/June power functions Simplify radical expressions with and without a variable. Identify perfect squares and perfect cubes. Classify numbers as whole numbers, integers, rational, irrational, real or imaginary. Differentiate between exact value and approximation. For example, 2 is the exact value and 1.4 is the approximate value. Evaluate expressions using the order of operations (P, E, M or D, A S) given values for variables. Multiply or divide radical expressions. Rationalize the denominator of a fraction. Add or subtract like radicals. Apply rules for radicals to real world situation. Solve radical and power equations. Write the symbolic form and sketch the graph of power functions, f(x) = x n, where n is an integer greater than three or a rational number between zero and one. Classify functions as having reflexive, rotational or no symmetry. Know the definition of the number i. Add, subtract and multiply imaginary/complex numbers. Solve quadratic equations that have complex solutions. Transition between real-world scenario, table, graph or equation to model a situation. Use representations of power functions (including rational powers) to analyze information, make predictions and solve problems. Write the domain or range of a power function as an inequality. cumulative exam semester two